Ultrasonic Ice Protection Systems: Analytical and ...

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Ultrasonic Ice Protection Systems: Analytical andNumerical Models for Architecture Tradeoff

Marc Budinger, Valérie Pommier-Budinger, Gael Napias, Arthur Costa daSilva

To cite this version:Marc Budinger, Valérie Pommier-Budinger, Gael Napias, Arthur Costa da Silva. Ultrasonic Ice Pro-tection Systems: Analytical and Numerical Models for Architecture Tradeoff. Journal of Aircraft,American Institute of Aeronautics and Astronautics, 2016, 53 (3), pp.680 - 690. �10.2514/1.C033625�.�hal-01861799�

https://hal.archives-ouvertes.fr/hal-01861799

https://hal.archives-ouvertes.fr

- 1 -

Ultrasonic ice protection systems: analytical and numerical models for

architecture trade-off

Marc Budinger(1)

, Valérie Pommier-Budinger(2)

, Gael Napias(2)

, Arthur Costa Da Silva(2)

(1) INSA Toulouse, Institut Clément Ader, Toulouse, 31077, France

(2) ISAE SUPAERO, Institut Supérieur de l'Aéronautique et de l'Espace, 31055, France

ABSTRACT

Protection systems against ice conventionally use thermal, pneumatic or electro-thermal solutions. However, they are

characterized by high energy consumption. This article focuses on low-consumption electromechanical deicing solutions

based on piezoelectric transducers. After a review of the state of the art to identify the main features of electromechanical

de-icing devices, piezoelectric transducer-based architectures are studied. Analytical models validated by numerical

simulations allow trend studies to be performed which highlight the resonance modes and the ultrasonic frequency

ranges that lead to low-consumption, compact ultrasonic deicing devices. Finally, de-icing systems widely studied with

bonded ceramics and de-icing systems less usual with Langevin pre-stressed piezoelectric transducers are compared and

a Langevin piezoelectric transducer-based device leading to an interesting compromise is tested.

Keywords: de-icing systems, electromechanical actuator, ultrasonic actuator, piezoelectric transducer, pre-stressed

Langevin actuator

1. INTRODUCTION AND STATE OF THE ART

1.1. Ice protection systems

Ice accretion on aircraft has been a well identified problem since the beginning of the 20th

century. It can lead to

decreased lift, increased drag, reduced thrust reduction, and risk of stalling or even engine failure owing to ice ingestion.

Icing occurs both during flight and on the ground. It has led to many aviation accidents, such as the Air Florida Boeing

B737 (1982), the American Eagle ATR 72 (1997), and the Air France Airbus A330 (2009). To ensure aircraft safety,

regulatory agencies, such as the CAA (Civil Aviation Authority [1]) and the FAA (Federal Aviation Administration [3]),

have established regulations for aircraft anti-icing and de-icing.

- 2 -

Current strategies for anti-icing and de-icing [1] can be chemical, thermal or mechanical - each having different

degrees of efficiency or environmental impact. The chemicals used for de-icing (ethylene, propylene glycol or diethylene

glycol) can lower the freezing point but require large volumes of fluids and induce environmental issues and premature

wear of the treated parts (especially corrosion). Thermal techniques are used for anti-icing and de-icing in flight and on

the ground by liquefaction and vaporization of the ice, but require either a large amount of hot air under pressure to be

bled from the engine or a large amount of energy to be provided by the electric grid for electro-thermal solutions.

Thermal solutions require around 4 kW/m² and the total amount of power required to de-ice a Boeing 787 with an

electrical de-icing system has been estimated at 76 kW [11]. Mechanical de-icing systems are low-energy solutions that

aim to break the accumulated ice by applying a mechanical pulse or vibrations to the structure to be protected. Pneumatic

systems are commonly used for their low cost but have a significant impact on the aerodynamics of the aircraft and

require maintenance. Recent efforts to develop electromechanical systems are justified by the potential of such systems in

terms of weight, durability and energy savings.

1.2. Electromechanical de-icing systems

Electromechanical deicing systems use electromagnetic actuators, piezoelectric actuators or shape memory

alloys. These systems are presented in [1] and [6] and their advantages and drawbacks are analyzed in Table 1.

This article focuses on actuation with piezoelectric technology, and especially on resonant piezoelectric

technologies, which have a better power/mass ratio than static solutions. The deeper insight into piezoelectric

de-icing systems presented in Table 2 allows a more detailed analysis to be carried out according to the frequency

range of the modes activated by the piezoelectric actuators and to the type of piezoelectric actuators.

Ramanathan et al. [7] proposed the use of ultrasonic shear waves at very high frequency (1 MHz). They performed

experiments with piezoelectric patches bonded to an isotropic plate with a layer of ice. The results indicate that the

actuators were able to de-ice the aluminum plate by melting the ice at the interface. Kalkowski et al. [8] analyzed the

frequency range for which wave-based technologies efficiently promote the delamination of ice with minimum power

requirements.

Venna et al. [9][10][11][12] used piezoelectric ceramics bonded onto plates and on the inner flat surface of a leading

edge structure to excite low frequency modes to delaminate ice (below 1000 Hz). They used analytical and numerical

- 3 -

models to identify the first modes for which the shear stress produced in the ice was greater than the shear stress that

would theoretically lead to delamination. The average de-icing time varied between 46 s and 280 s and increased as the

icing temperature decreased. Palacios [13] analyzed this result and found that the de-icing time seemed to show that the

de-icing was more probably caused by thermal effects than by shear stress. S. Struggl et al. [14] conducted the same kind

of analysis and experiments with piezoelectric ceramics bonded to a plate and on a leading edge structure to excite low

frequency modes (below 500 Hz). They also performed tests in an icing research tunnel and the de-icing was successful at

a frequency of 307 Hz.

Seppings [15] used a stack of thin piezo-electric discs held in compression by a bolt running through the center of the

stack and showed that the pre-stressed actuator driven at 20 kHz was more efficient than piezoelectric patches.

Palacios initiated many studies on de-icing systems [16][17][18][19][20][21] and tested several technologies. For

piezoelectric de-icing systems, he used piezoelectric patches to generate ultrasonic shear stress at high frequency (around

a few tens of kHz). He performed tests on plates [16][17] and on leading edges [18]. At such frequencies, the

delamination of the ice was instantaneous. He also tested an original design of a shear tube actuator driven at 300 V and

436 Hz [19]. In [20], experiments showed two main failures related to the bonding of the actuators: fracture of the

piezoelectric ceramic at the solder joint location and delamination between the ceramic and the host. To tackle this

problem, Palacios proposed optimizing the bonding of the supply wire on the ceramic and the bonding between the

piezoelectric actuators and the substrate to avoid concentrations of stresses [21]. In [22], he also investigated the effect of

hydrophobic coating combined with an ultrasonic deicing system and showed that the ice adhesion depended on the

substrate roughness.

More recently, Strobl [23] used multilayer piezoelectric patches at frequencies around 4 kHz and icephobic coating to

delaminate ice instantaneously on polished surfaces with a low supply voltage.

- 4 -

Technological solutions Main advantages Main drawbacks

Electromagnetic

Contactless possible, high

displacements possible

Low force density, electromagnetic pollution,

size of feeding electronics

Piezoelectric (PZT)

Force generation (good force/mass

ratio) even at high frequency,

energy consumption

Brittleness, small displacements

Shape Memory Alloy

(SMA)

Force generation in static Low dynamics, response time, energy

consumption

Table 1 – Comparison of electromechanical deicing systems

Comparison

criteria

Technological solutions Previous works

Main

advantages

Main drawbacks

Frequency

range

Static, Low Frequency

(Hz)

[9][10][11][12] [14]

Power

supply

Force of activation

Vibration (kHz)

[16][17] [18][19][20][21]

[22][23]

Fatigue

Waves (MHz) [7][8]

Energy

consumption

Technology

Bonded Piezoelectric

ceramics (PZT or

multilayers)

[9][10][11][12][15]

[16][17][18]

[20][21][21][22][14][23]

Easy to

implement

Brittle

Not easily

adaptable to

curved surfaces

Pre-stressed piezoelectric

transducer

[15]

Less brittle,

stress-

resistant

Frequency linked

to the size of the

transducer

Table 2 – Comparison of piezoelectric de-icing systems

- 5 -

1.3. Review of previous works, proposed architecture and objectives of present work

According to the previous analyses, the main features of piezoelectric de-icing devices are as follows:

- As regards the frequency range, previous studies on piezoelectric de-icing devices have shown that both low

frequencies and ultrasonic high frequencies can be excited to generate shear stress and to break ice. However, no

studies have been carried out to determine the best frequency range for which structural resonances maximize the

shear stress in the ice while minimizing the stress in the substrate and in the actuators. Consequently, a specific study

to determine the optimized frequency range is required and is proposed in this article.

- One other issue is the nature of the modes to be excited: both flexural and extensional modes can produce shear

stress in a structure. Thus, a specific study to determine the kind of modes that produce maximal shear stress will be

useful for the design of the de-icing system architecture.

- Regarding the actuation technology, this article will compare non-pre-stressed piezoelectric transducers (bonded

ceramics) and pre-stressed piezoelectric transducers (Langevin transducer) in terms of force-to-density ratio,

robustness, ease of integration in a curved leading edge and power consumption. Non-pre-stressed piezoelectric

transducers have been widely tested and examples off architectures can be found in [9][15][16][18][23]. Figure 1

shows two different architectures with a pre-stressed piezoelectric actuator, one exciting flexural modes, the other

exciting extensional modes. Both architectures lead to shear stress at the ice/substrate interface.

Figure 1 - Architecture for a de-icing system with a pre-stressed piezoelectric transducer: (a) Excitation of

flexural modes, (b) Excitation of extensional modes

The objectives of this paper are thus:

- to develop analytical models validated by numerical simulations and complemented by measurements in order to

perform trend studies highlighting the nature of the resonance modes and the frequency ranges leading to low-

consumption, compact piezoelectric de-icing devices.

Ice Aluminum substrate

Ice

Aluminum substrate

(a)

(b)

- 6 -

- to compare piezoelectric transducer-based architectures enabling an interesting compromise to be reached to

generate shear stress at the ice/substrate interface and to promote ice delamination and cracking without damaging the

actuator or the substrate.

2. FEASIBILITY OF PIEZOELECTRIC DE-ICING SYSTEMS BASED ON STRESS ANALYSIS

2.1. Study case

In this article, the study case is a simple plane rectangular plate of dimensions 290 × 200 × 1.5 mm3 that is covered

by a 2mm thick layer of ice. The panels of an aircraft airframe are usually supported by ribs and stiffeners and the

boundary conditions of such panels are close to clamped on all sides. However, the plates will be studied in the pinned

boundary condition in this section because this condition enables simple analytical expressions to be formulated to

estimate the stresses produced at the ice/substrate interface and because, at the high frequencies used in the study, the

deformations in the middle of the plate are similar for pinned and clamped boundary conditions (as illustrated in Figure

2).

Figure 2 - Comparison of two boundary conditions (clamped versus pinned) for the study of a plate at high

frequencies: displacements in the middle of the plate are sinusoidal in both cases

The mechanical properties of the ice considered for calculation were chosen so as to correspond to glaze ice and were

selected among the values presented in [24]. The ice and aluminum mechanical properties used for the analyses

performed in this article are shown in Table 3.

f = 12 254 Hz

Clamped boundary case

145mm middle of the plate

f = 11 434 Hz

145mm middle of

the plate

Ultrasonic ice protection systems: analytical models for architecture trade-off

- 7 -

Material Aluminum Ice

𝐸 (𝐺𝑃𝑎) 70 9.7

𝐺 (𝐺𝑃𝑎) 26 3.7

𝜈 (−) 0.33 0.30

𝜌 (𝑘𝑔/𝑚3) 2770 880

Table 3 –Mechanical properties of the study case materials

2.2. Stress generation

In order to choose the vibration modes that are the most suitable for de-icing by generation of stresses in a plate, four

types of “failure” modes of the ice/substrate interface were considered: failure owing to excessive tensile stress; failure

owing to excessive in-plane shear stress; failure owing to excessive out-of-plane shear stress and failure owing to

excessive out-of-plane tensile stress. Figure 3 shows a simplified scheme of the mechanisms and the interface failure

expected in each case. The values of ice strength are discussed in [25],[26],[27]. The parametric studies carried out by

Scavuzzo et al. [25] and by Jellinek [26] and the experiments performed by Laforte et al. [27] indicate that the adhesion

strength of ice depends mainly on the roughness of the accretion surface. Scavuzzos’s study also suggests that the

adhesion resistance to an out-of-plane stress (shear or tensile) depends, but to a lesser degree, on droplet momentum and

surface temperature. Laforte’s work shows that the adhesion resistance to an in-plane deformation (distortion or

elongation) varies with the ice thickness and Loughborough observed dependence of the strength on the nature of the

substrate [28]. Finally, Table 4 exposes the values of the properties presented in the references discussed. In this study,

the targeted application is the de-icing of aircraft flight control surfaces. For this kind of application, ice delamination by

shear is more efficient than breaking by tensile stress. This is why we focus on out-of-plane shear stress generation. For

the assessment of the different de-icing system architectures, we will compute the out-of-plane shear stress and ice will be

assumed to be de-bonded when the out-of-plane shear stress exceeds the critical adhesive strength of ice (considered to be

1 MPa for numerical applications of this paper). Moreover, to assess de-icing systems, the stress induced in the substrate

and in the piezoelectric ceramics will also be computed in order to quantify the risk of damage to the ceramics.


- 8 -

Figure 3 - Modes of failure of the ice-aluminum interface. a) Failure due to excessive in-plane tensile stress. b)

Failure due to excessive in-plane shear stress. c) Failure due to out-of-plane shear stress. d) Failure due to

excessive out-of-plane tensile stress

Ice Thickness (mm) 2 5 10

De-icing Tensile Strain ϵx,crit(μm/m) 500 420 280

De-icing In-Plane Shear Strain ϵxy,crit(μm/m) 700 350 212

De-icing Out-of-Plane Shear Stress τzx,crit(MPa) 1.10 – 0.55

De-icing Out-of-Plane Tensile Stress σz,crit(MPa) 1.20 – 0.95

Ice Tensile Strength (MPa) 3.1 – 0.7

Ice Compressive Strength (MPa) 5-25

Ice Shear Strength (MPa) 0.7

Table 4 –Adhesion properties of impact ice to aluminum surface with matte finish and its strength properties

([25],[26],[27])

2.3. Comparison of resonance modes on 1D models

The plate resonance modes used in the literature (section 1.2) are essentially in-plane extensional modes and out-of-

plane flexural modes. They generate stress corresponding to failure modes a) and c) in Figure 3. However, piezoelectric

actuators have limited displacement capacity. Consequently the comparison of these modes is made here in terms of

stresses generated for a given displacement. To simplify the analysis, several assumptions are used: support and ice are


- 9 -

considered as a thin multilayer beam (1D model), mode shapes are assumed to be identical to those of a uniform beam

and boundary conditions are simply supported as introduced in section 2.1. Figure 4 shows the beam under study where:

x is the transverse position along the beam of length a ;

n is the number of anti-nodes for the mode considered;

is the pulsation of the mode considered;

halu, hice, hn are respectively the thickness of the aluminum beam, the thickness of the ice beam and the position of the

neutral line for the flexural mode,

U(x) and W(x) are respectively the in-plane displacements (for extensional modes) and out-of-plane displacements

(for flexural modes);

calu , cice , alu and ice are respectively the Young modulus and the density for the aluminum beam and the ice.

a)

b)

Figure 4 –Element of the beam under study


- 10 -

For flexural modes, the position of the neutral line hncan be obtained by assuming that the tensile force in a section is

zero. This results in:

ℎ𝑛 =1

2

𝑐𝑎𝑙𝑢ℎ𝑎𝑙𝑢2 − 𝑐𝑖𝑐𝑒ℎ𝑖𝑐𝑒

2

𝑐𝑎𝑙𝑢ℎ𝑎𝑙𝑢 + 𝑐𝑖𝑐𝑒ℎ𝑖𝑐𝑒

(1)

Table 5 synthetizes the analytical equations derived from [29] to compute strains and stresses in the ice, in the

aluminum substrate and at the ice-substrate interface. The equations of the peak out-of-plane shear stress were obtained

by isolating an element of ice of thickness dx subjected to elastic forces, inertial forces and shear forces at the ice-

substrate interface. The resonance frequencies were obtained by the Rayleigh method [30] using the expression of the

strains to estimate the kinetic and potential energies.

Extensional modes Flexural modes

Displacement 𝑢(𝑥, 𝑡) = 𝑈(𝑥) 𝑠𝑖𝑛 𝜔𝑡 = 𝑈0 𝑠𝑖𝑛𝑛𝜋𝑥

𝑎𝑠𝑖𝑛 𝜔𝑡 𝑤(𝑥, 𝑡) = 𝑊(𝑥)𝑠𝑖𝑛 𝜔𝑡 = 𝑊0 𝑠𝑖𝑛

𝑛𝜋𝑥

𝑎𝑠𝑖𝑛 𝜔𝑡

𝑢(𝑥, 𝑡) = −𝑧𝜕𝑤

𝜕𝑥= 𝑈(𝑥)𝑠𝑖𝑛 𝜔𝑡

Peak tensile strain 𝜀𝑥 =

𝜕𝑈(𝑥)

𝜕𝑥= 𝑈0

𝑛𝜋

𝑎𝑐𝑜𝑠

𝑛𝜋𝑥

𝑎 𝜀𝑥 =

𝜕𝑈(𝑥)

𝜕𝑥= 𝑊0𝑧 (

𝑛𝜋

𝑎)

2

𝑠𝑖𝑛𝑛𝜋𝑥

𝑎

Peak ice tensile

stress in ice

𝜎𝑥 = 𝑐𝑖𝑐𝑒𝜀𝑥 = 𝑐𝑖𝑐𝑒𝑈0

𝑛𝜋

𝑎𝑐𝑜𝑠

𝑛𝜋𝑥

𝑎 𝜎𝑥 = 𝑐𝑖𝑐𝑒(ℎ𝑖𝑐𝑒 + ℎ𝑛) (

𝑛𝜋

𝑎)

2

𝑊0 𝑠𝑖𝑛𝑛𝜋𝑥

𝑎

Peak tensile stress

in aluminum

𝜎𝑥 = 𝑐𝑎𝑙𝑢𝜀𝑥 = 𝑐𝑖𝑐𝑒𝑈0

𝑛𝜋

𝑎𝑐𝑜𝑠

𝑛𝜋𝑥

𝑎 𝜎𝑥 = 𝑐𝑎𝑙𝑢(ℎ𝑎𝑙𝑢 − ℎ𝑛) (

𝑛𝜋

𝑎)

2

𝑊0 𝑠𝑖𝑛𝑛𝜋𝑥

𝑎

Peak out-of- plane

shear stress at the

ice/aluminum

interface

𝜏𝑥𝑧 = (𝜌𝑖𝑐𝑒𝜔2 − 𝑐𝑖𝑐𝑒 (𝑛𝜋

𝑎)

2

) ℎ𝑖𝑐𝑒𝑈0 𝑠𝑖𝑛𝑛𝜋𝑥

𝑎 𝜏𝑥𝑧 = 𝑐𝑎𝑙𝑢 (

𝑛𝜋

𝑎)

3 (ℎ𝑎𝑙𝑢 − ℎ𝑛)2 − ℎ𝑛2

2𝑊0 𝑐𝑜𝑠

𝑛𝜋𝑥

𝑎


- 11 -

Angular frequency

𝜔 = 𝜋𝑛

𝑎√

𝑐𝑖𝑐𝑒ℎ𝑖𝑐𝑒 + 𝑐𝑎𝑙𝑢ℎ𝑎𝑙𝑢

𝜌𝑖𝑐𝑒ℎ𝑖𝑐𝑒 + 𝜌𝑎𝑙𝑢ℎ𝑎𝑙𝑢

𝜔 = 𝜋2 (

𝑛

𝑎)

2

√𝐸𝐼

𝜌𝑖𝑐𝑒ℎ𝑖𝑐𝑒+𝜌𝑎𝑙𝑢ℎ𝑎𝑙𝑢 with

𝐸𝐼 =𝑐𝑎𝑙𝑢

3(ℎ𝑛

3 + (ℎ𝑎𝑙𝑢 − ℎ𝑛)3)

+𝐶𝑖𝑐𝑒

3((ℎ𝑛 + ℎ𝑖𝑐𝑒)3 − ℎ𝑛

3)

Table 5 – 1D modes equations

These analytical equations show that:

- for extensional modes, the maximum tensile stress in the substrate or the ice is located on the displacement nodes and

the maximum out-of-plane shear stress at the ice-substrate interface is located on the displacement antinodes,

- for flexural modes, the maximum out-of-plane shear stress is located on the displacement nodes.

Figure 5 also compares the extensional and flexural modes, particularly their ability to generate shear stress at the ice-

substrate interface. It also gives the tensile stress in the ice and in the aluminum substrate. It shows that, for a given

frequency and for a given displacement, the shear stress level at the ice-substrate interface is smaller for extensional than

for flexural modes, while the tensile stress in the aluminum substrate is almost the same. Thus, to generate ice

delamination while minimizing the displacement of the piezoelectric actuators, it is more interesting to excite flexural

modes. This is done for example by architecture a of Figure 1. Another conclusion that can be drawn from Figure 5 is that

it is more favorable to work at high frequencies: the higher the frequency, the higher the shear stress. However, the

frequency of use may be limited by other criteria such as power supply issues.

Note: the results of Figure 5 were obtained for a 2 mm thick ice layer. The expression of out-of-plane shear stress xz

shows that this stress would be maximum for a null position of the neutral line (hn=0), which implies an optimal ice

thickness hice:

ℎ𝑖𝑐𝑒 = ℎ𝑎𝑙𝑢√𝑐𝑎𝑙𝑢

𝑐𝑖𝑐𝑒

(2)


- 12 -

Relation (2) gives an optimal ice thickness of 4.5 mm for a 1.5 mm thick aluminum substrate. However, for future

calculations we chose a 2 mm thick ice layer, less attractive in terms of stress generation, but more realistic for the

targeted application (de-icing of aircraft flight control surfaces).

Figure 5 – Comparison of extensional and flexural modes

2.4. Shear stress estimation on 2D models for flexural modes

The previous section gave 1D models of beam type structures. In this section, stresses are expressed for 2D plate type

geometries. Following the conclusions of the study for 1D models, stresses will be computed only for flexural modes. For

this type of movement, each point of the plate is considered to have a vertical displacement ww in its x and y directions

such that 𝑤 =w = w(x, y, t). We assume that the displacement w(x, y, t) can be approximated by the analytical solution

for flexural modes of a homogeneous plate [30]. Table 6 synthetizes the analytical equations to compute the strains, the

shear stress at the ice-substrate interface and the tensile stresses in the aluminum substrate and in the ice. n is the number

of anti-nodes on the length for the considered mode and m the number of anti-nodes on the width.

10-2

10-1

100

101

102

103

10-5

10-4

10-3

10-2

10-1

100

101

102

Frequency (kHz)

Sh

ea

r (.

..)

an

d te

nsile

(_

__

) S

tre

ss (

MP

a/µ

m)

Stress vs frequency

Shear at ice/substrate interface (flexural mode)

Tensile in aluminum substrate (flexural mode)

Tensile in ice (flexural mode)

Shear at ice/substrate interface (extensional mode)

Tensile in aluminum substrate (extensional mode)

Tensile in ice (extensional mode)


- 13 -

Flexural modes

Displacements 𝑤(𝑥, 𝑦, 𝑡) = 𝑊0 sin𝑛𝜋𝑥

𝑎sin

𝑚𝜋𝑦

𝑏sin 𝜔𝑡

𝑢(𝑥, 𝑦, 𝑡) = −𝑧𝜕𝑤

𝜕𝑥

𝑣(𝑥, 𝑦, 𝑡) = −𝑧𝜕𝑤

𝜕𝑦

Strains

Peak tensile strain

(Sxx)

𝜀𝑥 = 𝑊0𝑧 (𝑛𝜋

𝑎)

2

sin𝑛𝜋𝑥

𝑎sin

𝑚𝜋𝑦

𝑏

𝜀𝑦 = 𝑊0𝑧 (𝑚𝜋

𝑏)

2

sin𝑛𝜋𝑥

𝑎sin

𝑚𝜋𝑦

𝑏

Peak in-plane

shear strain (Sxy)

𝛾𝑥𝑦 =1

2(

𝜕𝑢

𝜕𝑦+

𝜕𝑣

𝜕𝑥) = −𝑧

𝜕2𝑤

𝜕𝑥𝜕𝑦= −𝑧𝑊0

𝑛𝜋

𝑎

𝑚𝜋

𝑏cos

𝑛𝜋𝑥

𝑎cos

𝑚𝜋𝑦

𝑏

Stresses

Peak ice tensile

stress (Txx)

𝜎𝑥 =𝑐𝑖𝑐𝑒

1 − 𝜈𝑖𝑐𝑒2

(ℎ𝑖𝑐𝑒 + ℎ𝑛) ((𝑛𝜋

𝑎)

2

+ 𝜈 (𝑚𝜋

𝑏)

2

) 𝑊0 sin𝑛𝜋𝑥

𝑎sin

𝑚𝜋𝑦

𝑏

Peak aluminum

tensile stress (Txx)

𝜎𝑥 =−𝑐𝑎𝑙𝑢

1 − 𝜈𝑎𝑙𝑢2

(ℎ𝑎𝑙𝑢 − ℎ𝑛) ((𝑛𝜋

𝑎)

2

+ 𝜈 (𝑚𝜋

𝑏)

2

) 𝑊0 sin𝑛𝜋𝑥

𝑎sin

𝑚𝜋𝑦

𝑏

Peak in-plane

shear stress (Txy)

𝜏𝑥𝑦 = −(ℎ𝑖𝑐𝑒 + ℎ𝑛)𝑐𝑖𝑐𝑒

1 + 𝜈𝑖𝑐𝑒

𝑊0

𝑛𝜋

𝑎

𝑚𝜋

𝑏cos

𝑛𝜋𝑥

𝑎cos

𝑚𝜋𝑦

𝑏

Peak out-of- plane

shear stress (Txz)

𝜏𝑥𝑧 =𝑐

1 − 𝜈2((

𝑛𝜋

𝑎)

2

+ (2 − 𝜈) (𝑚𝜋

𝑏)

2

)𝑛𝜋

𝑎

(ℎ𝑎𝑙𝑢 − ℎ𝑛)2 − ℎ𝑛2

2𝑊0 𝑐𝑜𝑠

𝑛𝜋𝑥

𝑎𝑠𝑖𝑛

𝑚𝜋𝑦

𝑏

Table 6 –2D flexural modes equations

These equations are validated by a Finite Element analysis performed for the geometry of the study case (halu = 1.5

mm, calu = 70 GPa, hice = 2 mm, cice = 9.7 GPa, hn = 0.48 mm, a=290 mm, b = 200 mm). Table 7 shows the mode for n=13


- 14 -

and m=5 of frequencies around 15 kHz, which is an intermediate frequency among the frequencies usually used for tests

with piezoelectric ceramics bonded on substrate. The comparison of analytical and numerical results shows a difference

of less than 8% and validates the analytical models developed.

Flexural mode

n=13

m=5

Analytical results Numerical results

Resonance frequency 15554 Hz 14732 Hz

Maximum tensile stress in the ice layer 0.57 MPa/µm 0.52 MPa/µm

Maximum shear stress at the ice/substrate

interface

0.134 MPa/ µm 0.144 MPa/µm

Table 7 – Comparison of analytical equations and Finite Element Analysis

2.5. Frequency range for piezoelectric de-icing systems

The equations of Table 6 will be used to study the feasibility of de-icing systems with piezoelectric actuators and to

highlight the frequency ranges leading to efficient piezoelectric deicing devices. The study will be performed for the

study case of section 2.1, with a number of anti-nodes in the length varying between 1 and 25 and a number of anti-nodes

in the width varying between 1 and 15.

Figure 6 and Figure 7 show that the shear stress per µm of displacement at the ice/substrate interface and the tensile

stress per µm in aluminum or ice increase with the number of anti-nodes and with frequency. One requirement for de-

icing systems is to remove ice without stressing the structure on which it is deposited. This means that de-icing systems

must maximize stress at the ice/substrate interface while minimizing stress in the structure. The ratio of tensile stress in

aluminum to shear stress at the ice/substrate interface represented in Figure 8 allows the frequency range to be found for


- 15 -

which the de-icing systems are the most efficient in meeting this requirement and shows that ultrasonic frequencies,

higher than 20 kHz, are more favorable.

Figure 6 - Flexural resonance frequencies and stresses for the study case versus the number of anti-nodes

Figure 7 - Shear stress per µm according to frequency for flexural modes

Number m of anti-node (200 mm)

Num

ber

n o

f anti-n

ode (

290 m

m)

Frequency (kHz)

5 10 15

5

10

15

20

25

10

20

30

40

50

60

70


Num

ber

n o

f anti-n

ode (

290 m

m)

Shear stress (MPa/µm)

5 10 15

5

10

15

20

25

0.2

0.4

0.6

0.8

1

1.2


Num

ber

n o

f anti-n

ode (

290 m

m)

Tensile stress (MPa/µm) in ice

5 10 15

5

10

15

20

25

0.5

1

1.5

2


Num

ber

n o

f anti-n

ode (

290 m

m)

Tensile stress (MPa/µm) in aluminium

5 10 15

5

10

15

20

25

1

2

3

4

5

6


- 16 -

Figure 8 - Aluminum stress / shear stress according to frequency for flexural modes

3. EVALUATION OF DIFFERENT ARCHITECTURES OF PIEZOLECTRIC DE-ICING SYSTEMS

The previous section highlighted the type of modes (flexural modes) and the frequency range (ultrasonic) of the

resonant modes to be excited to lead to ice delamination. This section aims to assess the type of piezoelectric actuators to

be used. Two kinds of actuators are compared: patch type actuators, directly bonded on to the structure to be activated,

and Langevin pre-stressed actuators in the configuration Figure 1a.

3.1. Methodology for evaluating piezoelectric deicing systems

The proposed methodology for evaluating the 2 different architectures of piezoelectric de-icing systems is divided into

2 main phases:

1. Computation of a reduced model (analytically or numerically) of the chosen architecture of the de-icing system

connected to the surface with the layer of ice. Computation of the maximal tensile stress per µm within the PZT

ceramics and of the shear stress per µm at the ice/substrate interface. All these results are computed for the

resonance mode for which the coupling between the piezoelectric actuator and the structure is the best, i.e. for

which the required voltage will be the lowest.

2. Computation of the displacement required to generate the minimal stress value and of the voltage that leads to the

required displacement. As the piezoelectric de-icing systems are resonant systems, this result depends strongly on

the damping of the structure with the ice.


- 17 -

3.1.1. Reduced model of systems with piezoelectric actuators

This section details the computations of the two design methodology phases. These details are extracted from [34].

The reduced model of a structure with piezoelectric actuators can be made for one mode with a mechanical equation and

an electrical equation:

VCNqq

NVKqqDqM

oC

s

(3)

where q is the modal displacement, M the modal mass, K the modal stiffness, qc the electrical charge, V the voltage, Ds

the modal damping, the modal electromechanical coupling factor, and Co the modal turned-off capacity.

This model can be computed analytically for simple geometries or with multiphysics Finite Element software (such as

COMSOL©, ANSYS© or ABAQUS©) that allows calculations with piezoelectric elements. If the computations are

carried out with short-circuited piezoelectric patches, V=0 and the equations become:

θqq

NVKqqDqM

C

s

(4)

which means that

𝑁 =𝑞𝑐

𝑞

(5)

and for the resonance:

𝑁 =𝑞𝑐

𝑞

(6)

For structures with low damping,

𝑄𝑚 ≈𝐾

𝜔𝐷𝑠

(7)

Consequently, if the displacement required to de-bond ice is known for a resonance mode, the voltage that generates this

displacement is given by:


- 18 -

𝑄𝑚 ≈𝐾

𝜔𝐷𝑠

(8)

3.1.2. Design drivers of piezoelectric actuators

The electromechanical coupling factor N describes the ability of the piezoelectric actuators to generate a force on the

degree of freedom q for a given resonance mode. Moreover, stresses are proportional to displacements of the degrees of

freedom. We chose to compute the electromechanical coupling factor for the point characterized by the largest

displacement (in-plane or out-of-plane depending on excited modes). The electromechanical coupling factor may be

influenced by: the mode of the piezoelectric ceramic of the transducer (mode 31 for the bonded patch and mode 33 for the

Langevin transducer), the dimensions and positioning of the ceramic relative to the nodes and antinodes, and the presence

of adhesive.

A piezoelectric transducer may have several operational limits [35]: maximum voltage to avoid depolarization by

application of an excessive electric field (400 V/mm of ceramic thickness), maximum stress in the ceramics to avoid

failure (about 24 MPa in extension for dynamic applications and for non-pre-stressed ceramics) and maximum

temperature to avoid reaching the Curie temperature, which leads to depolarization. The thermal limit will not be

considered here because of the very low ambient temperatures.

As shown in Equation 30, the displacement at resonance depends on the damping of the structure, characterized by a

mechanical quality coefficient. This coefficient is highly dependent on the boundary conditions and on the complexity of

the assembly. To assess the different architectures, we assume a value of Qm equal to 100 here, which corresponds to a

damping coefficient of 0.5%.

3.2. Piezoelectric de-icing system with bonded ceramics

The first configurations studied here are inspired directly from the work of Palacios ([17][18][20][21]) because he

experimentally proved their ability to provide instantaneous de-icing even for untreated surfaces (without polishing,

without hydrophobic or icephobic coating). The actuator configurations consist of one or more PZT disks glued onto the

surface to be de-iced. Palacios explained that ice delamination occurs for frequencies near the first radial extensional

mode of the piezoelectric disk.


- 19 -

Two simple configurations will be processed in this section:

Free axisymmetric disks described in [36] (Figure 9a). This study, which allows simple 2D Finite Element analyses

because of the symmetry, will help the phenomena involved to be understood on a 2D model and allows the

parameters that are negligible for future simulations in 3D (e.g. glue thickness) to be estimated, thus avoiding fine

meshes of very thin layers and heavy 3D models.

Clamped plates with the dimensions given in section 2.1 (Figure 9b). This geometry will allow a comparison with

the architecture based on a Langevin transducer, which will be studied in the next section. A volume of ceramic

similar to that of the Langevin transducer is chosen in order not to bias the comparison.

Figure 9 - Studied configurations with bonded ceramics (free disk and clamped plate)

We start by the study of the free axisymmetric disks. Figure 10 describes the geometry studied by Soltis under the

direction of Palacios [36]. We performed studies step by step (PZT ceramic only, aluminum plate only, PZT/aluminum

plate, PZT/aluminum plate /ice) to understand the principle of ice delamination.

Figure 10 - Axisymmetric configuration with bonded ceramics (disk)

(a) (b)


- 20 -

The study of the piezoelectric ceramic alone shows that the extensional radial frequency of the PZT disk is around

29.9 kHz. As Palacios recommends studying the modes around the extensional radial mode of the PZT disk, extensional

and flexural modes around this frequency are preferentially studied.

We first look at the modal shape of these 2 modes. Figure 11(a)(b)(c) shows the modal shapes of the aluminum plate

alone (case (a)), the aluminum plate with the piezoelectric disk (case (b)) and the aluminum plate with the piezoelectric

disk and ice (case (c)). These modal shapes are represented for the extensional radial frequency close to that of the PZT

disk. With a PZT disk bonded on the aluminum plate (with or without ice), the configuration is not symmetric about one

plane normal to the axisymmetric axis and the radial mode thus generates both radial and axial displacements. Figure

11(d) shows the modal shape of the flexural frequency close the extensional radial frequency of the PZT disk for the case

of aluminum plate with piezoelectric disk and ice. The axial displacements generated by the flexural mode are phased-

shifted by a quarter of a wavelength compared to the axial displacements generated by the extensional mode. Such axial

displacements generated by the flexural and extensional modes and phased-shifted explain why this configuration excited

by a sweep in frequency is favorable to de-ice the entire surface: nodes of the axial displacements for which shear stress

are important are spread over the entire surface.

Then Table 8 gives (i) the parameters of the reduced model for the flexural and extensional modes, including the

electromechanical force factor, and (ii) the computation results of the shear stresses required to de-bond the ice. The

extensional mode has a high electromechanical force factor; the transducer is well-coupled with the structure. For a

quality factor of 100, the required displacement to de-bond the ice is 9.22µm, which induces a voltage of 124 V - which is

reasonable - and a tensile stress in the aluminum plate of nearly 42 MPa – which is quite high. For the flexural mode, the

electromechanical force factor is much smaller but, as the stiffness is also smaller, the required displacement to de-bond

the ice is 7.72µm and the required voltage is 88 V. The tensile stress in the aluminum plate is also around 42 MPa, similar

to the extensional mode.


- 21 -

(a) Extensional mode for Alu (28 kHz)

(b) Extensional mode for Alu+PZT (28.5 kHz)

(c) Extensional mode for Alu+PZT+Ice (26.2 kHz)

(d) Flexural mode for Alu+PZT+Ice (27.7 kHz)

Figure 11 – Axial and radial displacements for axisymmetric configuration

-1,0

-0,5

0,0

0,5

1,0

1,5

0 0,05 0,1 0,15 0,2

No

rmal

ize

d d

isp

lace

me

nt

Radial position (m)

Axial

Radial

-1,0

-0,5

0,0

0,5

1,0

1,5

0 0,05 0,1 0,15 0,2

No

rmal

ize

d d

isp

lace

me

nt

Radial position (m)

Axial

Radial

-1,0

-0,5

0,0

0,5

1,0

1,5

0 0,05 0,1 0,15 0,2

No

rmal

ize

d d

isp

lace

me

nt

Radial position (m)

Axial

Radial

-0,6-0,4-0,20,00,20,40,60,81,01,2

0 0,05 0,1 0,15 0,2

No

rmal

ize

d d

isp

lace

me

nt

Radial position (m)

Axial

Radial


- 22 -

Computed electromechanical parameters of the reduced model and stresses per µm

(results of Finite Element Analysis)

Extensional

mode at 26.2

kHz

Flexural

mode at 27.2

kHz

Modal mass M Kg 0.12 0.01

Modal stiffness K N/m 3.18E+09 3.74E+08

Modal electromechanical coupling factor N N/V 2.37 0.33

Shear stress xz /µm at ice/substrate interface Txz/µm MPa/µm 0.11 0.13

Tensile stress xx /µm in PZT Txx/µm MPa/µm 4.55 5.45

Ratio Txx/Txz

- 41.95 42.07

Displacements and voltages required to de-bond the ice

Shear stress required to de-bond ice Txz MPa 1 1

Displacement required to de-bond ice Uo µm 9.22 7.72

Tensile stress in PZT Txx PZT MPa 41.95 42.07

Quality factor Qm - 100 100

Voltage supply U V 124 88

Table 8 – Computation results for the axisymmetric configuration

in the case of bonded PZT+Aluminum Plate+Ice

The next study is the study case (see section 2.1) of this article: a rectangular aluminum plate of dimensions 290x200x1.5

mm3. We consider a square piezoelectric ceramic of dimensions 60x60x2.5 mm

3 bonded in the center of the plate, the

volume of which is similar to that of the bolt-clamped transducer that will be used in the next section. The extensional

radial frequency of the PZT ceramic is around 31.8 kHz. The resonance extensional frequency of the aluminum

plate/ice/PZT assembly close to that frequency is 33.2 kHz. For this extensional frequency, Figure 12 shows the in-plane

and out-of-plane displacements. In-plane magnitudes are 5.6 times higher than out-of-plane magnitudes. The computed


- 23 -

electromechanical force factor is 1.2 N/V. Obtaining sufficient stresses to achieve delamination requires a voltage of

about 86 V and also displacement of 21 µm, which generates a very high stress level in the piezoelectric ceramic.

Palacios emphasizes this issue, which leads to the breakdown of ceramics, in numerous works ([36],[37]).

a) In-plane displacements

b) Out-of-plane displacements

Figure 12 – Displacements for the extensional frequency (33.20 kHz) close to radial frequency of the ceramic

(rectangular configuration with a bonded piezoelectric ceramic)



Extensional mode

at 33.2 kHz

Modal mass M Kg 0.01

Modal stiffness K N/m 4.90E+08

Modal electromechanical coupling factor N N/V 1.2

Shear stress xz /µm at ice/substratum interface Txz/µm MPa/µm 0.05

Tensile stress xx /µm in PZT Txx/µm MPa/µm 3.33

Ratio Txx/Txz

- 70

Displacements and voltages required to de-bond ice

Shear stress required to de-bond ice Txz MPa 1

Displacement required to de-bond ice U0 µm 21

Tensile stress in PZT Txx PZT MPa 70


- 24 -

Quality factor Qm - 100

Voltage supply U V 86

Table 9 – Computation results for the rectangular configuration

in the case of bonded piezoelectric ceramic+aluminum plate+ice

3.3. Piezoelectric de-icing system with Langevin transducers

In order to excite flexural modes of the surfaces to be protected, the architecture of Figure 1(a) is studied here. A bolt-

clamped Langevin transducer (Figure 13) is thus connected to the plate described in section 2.1 through a spacer ring of

length 10 mm. The extensional resonance frequency of the transducer alone is 40.44 kHz. For the Langevin

transducer/aluminum plate/ice assembly, the resonance frequency for which the delamination of the ice occurs with the

lowest supply voltage is 46.857 kHz. For that frequency, the electromechanical force factor is 1.25 N/V. Obtaining

sufficient shear stresses to achieve delamination requires a voltage of about 123 V and the tensile stress in the

piezoelectric ceramics is then 9.8 MPa, which is much less than for architectures with bonded piezoelectric ceramics.

Figure 13 - Bolt-clamped Langevin transducer and its first extensional resonance mode

Figure 14 – Study case: bolt-clamped Langevin transducer connected to the plate


- 25 -

a) Out-of-plane displacements

b) Shear stress at the ice/substrate interface

Figure 15 – Displacements for the flexural mode (46.86 kHz) (rectangular configuration with a Langevin

transducer)



Results at 46.857 kHz

Modal mass M Kg 0.0096

Modal stiffness K N/m 8.4e+09

Modal electromechanical coupling factor N N/V 1.25

Shear stress xz /µm at ice/substrate interface Txz/µm MPa/µm 0.55

Tensile stress xx /µm in PZT Txx/µm MPa/µm 5.3

Ratio Txx/Txz

- 9.63

Displacements and voltages required to de-bond ice

Shear stress required to de-bond ice Txz MPa 1

Displacement required to de-bond ice W0 µm 1.83

Tensile stress in PZT Txx PZT MPa 9.8

Quality factor Qm - 100

Voltage supply U V 123

Table 10 – Computation results for the rectangular configuration

in the case of Langevin transducer+spacer+aluminum plate+ice


- 26 -

3.4. Comparison of the 2 architectures

It is possible to compare the actuating architectures according to several criteria:

The limitations of use owing to stresses in PZT ceramics. The advantage of the architecture with Langevin

transducers is that stresses in the ceramics are only 9.8 MPa, which is 7 times less than for the architecture with

bonded ceramics. Moreover, the risk of mechanical failure is much lower for Langevin transducers than for

bonded ceramics as their pre-stressed structure enables them to withstand higher stresses in operation.

Power consumption is mainly due to mechanical losses during resonance and thus to the mechanical energy of

elastic deformation. This energy is 7.8 times greater for the architecture with bonded ceramics because it

requires much greater deformations (21 microns against 1.83 microns).

The size of the power electronics is dependent on the power consumption but also on the capacitive energy

stored in PZT ceramics. Power devices with good efficiency, such as resonant inverters, have inductors which

are all the larger when the capacitive energy is high. This energy is 2.2 times greater for the architecture with

bonded ceramics because, even if the voltage is lower, the capacitance is greater.

3.5. Experimental validation

Tests were performed on the solution with the Langevin transducer, which seems the most promising if we

consider a criterion that minimizes the energies involved and the stresses in the piezoelectric ceramics. A clamped

aluminum plate without coating was covered with 2 mm of ice (glaze-type ice obtained in a freezing chamber). The

Langevin transducer was then supplied with a voltage of around 46kHz frequency and 150V and 180V amplitude.

Figure 16 shows the results achieved during the experiment. The delamination of the ice started to occur at 150 V

and was even more visible at 180 V. The difference between the estimated voltage and the voltage measured during

the experiment may come from the uncertainty on the quality factor, the non-linearity and the uncertainties on the

shear stress leading to ice delamination (assumed to 1 MPa for computations).


- 27 -

(a) 0V

(b) 150 V

(c)180 V

Figure 16 – Experimental results for the configuration Langevin transducer+spacer+aluminum plate+ice and

excitation of the flexural mode of 46.86 kHz frequency

4. CONCLUSION

This article has aimed to compare different architectures of de-icing systems based on piezoelectric actuators and on

the use of structural resonance modes. The analytical models of the aluminum substrate with ice have shown that it is

more interesting to excite flexural modes than extensional modes to maximize the shear stress at the substrate/ice

interface. These models also highlighted that ultrasonic frequencies over 20 kHz allowed the shear stress to be maximized

for a given displacement, thus avoiding fatigue in the substrate and limiting breakdown of the actuators. The modeling of

the substrate and the actuators by finite element models highlighted the interest of Langevin type actuators with regard to

the resistance to mechanical stress and the mechanical and electrical energies involved in this kind of de-icing system.

Tests validated the efficiency of ice delamination with an architecture based on Langevin type actuators and favoring

structural flexural modes. These experiments also confirm the interest of studying such solutions more intensively.

5. REFERENCES

[1] Civil Aviation Authority. Aircraft Icing Handbook, 2000

[2] Z. Goraj, An overview of the deicing and anti-icing technologies with prospects for the future, 24th Congress of

International Council of the Aeronautical Sciences, 29 August-3 September, Yokohama, Japan, 2004

[3] Federal Aviation Administration. Advisory Circular AC 91-74A - Pilot Guide: Flight in Icing Conditions, 2007


- 28 -

[4] O. Meier, D. Schloz, A handbook method for the estimation of power requirements for electrical de-icing systems,

DLRK, Hamburg, 2010

[5] D. Kevin, L.B. Murphy, Aircraft deicing and anti-icing equipment, Safety Advisor, AOPA Air Safety Advisor

Wheather, Vol.2, pp.1-10, 2004

[6] R. Myose, W. Horn, Y. Hwang, J. Herrero et al., Application of Shape Memory Alloys for Leading Edge Deicing,

SAE Technical Paper 1999-01-1585, 1999, doi:10.4271/1999-01-1585.

[7] S. Ramanathan; V.V. Varadhan, V.K. Varadhan, De-Icing of Helicopter Blades Using Piezoelectric Actuators,

Smart Structures and Materials, Smart Electronics and MEMS, 281 (June 21, 2000), pp. 354-363, 2000

[8] M.K. Kalkowski; T.P. Waters, E. Rustighi, Removing surface accretions with piezo-excited high-frequency

structural waves, Proc. SPIE 9431, Active and Passive Smart Structures and Integrated Systems 2015, San Diego,

California, United States, March 08, 2015

[9] S.V. Venna, Y.J. Lin, In-Flight De-Icing Self-Actuating Wing Structures with Piezoelectric Actuators, Proceedings

of American Society of Mechanical Engineers/International Mechanical Engineering Congress and Exposition 2002,

ASME Press, New York, NY, pp. 237–245., 2002

[10] S.V. Venna, Y.J. Lin, Development of Self-Actuating In-Flight De-Icing Structures with Power Consumption

Considerations, Proceedings of the American Society of Mechanical Engineers International Mechanical Engineering

Congress and Exposition 2003, ASME Press, New York, NY, pp. 45–53, 2003

[11] S.V. Venna, Y.J. Lin, Mechatronic development of self-actuating in-flight deicing systems, IEEE/ASME

Transactions on Mechatronics, vol.11(5), pp.585-592, 2006

[12] S.V. Venna, Y.J. Lin, G. Botura, Piezoelectric Transducer Actuated Leading Edge De-Icing with Simultaneous

Shear and Impulse Forces, Journal of Aircraft, Vol. 44, pp.509-515, 2007

[13] J. Palacios, E. Smith, J. Rose, R. Royer, Instantaneous De-Icing of Freezer Ice via Ultrasonic Actuation, AIAA

journal, vol. 49(6), 1158-1167.

[14] S. Struggl, J. Korak, C. Feyrer, A basic approach for wing leading deicing by smart structures, Sensors and Smart

Structures Technologies for Civil, Mechanical, and Aerospace Systems, Vol. 7981, 2011

[15] R. Seppings, Investigation of Ice Removal From Cooled Metal Surfaces, Mechanical Engineering Department,

Imperial College London, 2006


- 29 -

[16] J.L. Palacios, Design, Fabrication, and Testing of an Ultrasonic De-Icing System for Helicopter Rotor blades, PhD

Thesis, The Pennsylvania State University, Department of Aerospace, May 2008

[17] J.L. Palacios, E.C. Smith, J. Rose, Investigation of An Ultrasonic Ice Protection System For Helicopter Rotor

Blades, Annual Forum Proceedings - AHS International 64th Annual Forum, Vol. 1, pp. 609-618, 2008

[18] J.L. Palacios, E.C. Smith, J. Rose, R. Royer, Ultrasonic De-Icing of Wind Tunnel Impact Icing, Journal of Aircraft,

Vol. 48(3), pp. 1020- 1027, 2011

[19] J.L. Palacios, E.C. Smith, Dynamic Analysis and Experimental Testing of Thin-Walled Structures Driven by Shear

Tube Actuators, AIAA 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference,

18 April-21 April, 2005

[20] A. Overmeyer, J. Palacios, E. Smith, R. Royer, Rotating Testing of a Low-Power, Non-Thermal Ultrasonic De-icing

System for Helicopter Rotor Blades, SAE Technical Paper, International Conference on Aircraft and Engine Icing and

Ground Deicing, June 13-17 2011, Chicago, IL 2011

[21] A. Overmeyer, J. Palacios, E. Smith, Actuator Bonding Optimization and System Control of a Rotor Blade

Ultrasonic Deicing System, 53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials

Conference, 23 April-26 April, 2012

[22] S. Tarquini, C. Antonini, A. Amirfazli, M. Marengo, J. Palacios, Investigation of ice shedding properties of

superhydrophobic coatings on helicopter blades, Journal of Cold Regions Science and Technology, Vol. 100 , pp. 50–58,

2014

[23] T. Strobl, S. Storm, M. Kolb, J. Haag, M. Hornung, Development of a Hybrid Ice Protection System based on

Nanostructured Hydrophobic Surfaces, ICAS Conference, St. Petersburg, Russia, 7-12 September, 2014

[24] J.J. Petrovic, Mechanical Properties of Ice and Snow, Journal of Material Science, Vol. 38, 2003.

[25] R.J. Scavuzzo, M. L. Chu, Structural Properties of Impact Ices Accreted on Aircraft Structures, NASA Contractor

Report 179580, 1987

[26] HH. G Jellinek, Adhesive Properties of Ice – Part II, 1960

[27] C. Laforte, J. Laforte, Deicing Strains and Stresses of Ice Substrates, Journal of Adhesion Science and Technology

26 (2012) 603-620

[28] D.L Loughborough, E.G. Hass, Reduction of Adhesion of Ice to De-icer Surfaces, Journal of Aeronautical Sciences,

Vol.13(3): pp. 126-134, 1946


- 30 -

[29] S. Timoshenko, Strength of Materials, D. Van Nostrand, 1955

[30] M. Géradin, D.J. Rixen, Mechanical vibrations: theory and application to structural dynamics. John Wiley & Sons,

2014

[31] R.D. Blevins, Formulas for Natural Frequency and Mode Shape, 2001.

[32] J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2°ed. 2004

[33] J.N. Reddy, Energy and Variational Methods in Applied Mechanics: With an Introduction to the Finite Element

Method,1984

[34] V. Pommier-Budinger, M.Budinger, Sizing optimization of piezoelectric smart structures with meta-modeling

techniques for dynamic applications, International Journal of Applied Electromagnetics and Mechanics, Vol.46(1),

pp.195-206.

[35] D.A. Berlincourt, H.H.A. Krueger, Behaviour of Piezoelectric Ceramics under Various Environmental and

Operation Conditions of Radiating Sonar Transducers, Technical Publication TP-228, Morgan Electro-Ceramics.

[36] J.T. Soltis, Design and testing of an erosion resistant ultrasonic de-icing system for rotorcraft blades, Thesis in

Aerospace Engineering at Pennsylvania State University, 2013.

[37] A.D. Overmeyer, Actuator bondline optimization and experimental deicing of a rotor blade ultrasonic deicing

system, Thesis in Aerospace Engineering at Pennsylvania State University, 2012.

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